1) as an obligatory fast, like the days of Ramadhaan, either in Ramadhaan or making the days up, fasting as an expiation, or as an alternative to slaughtering, this is permissible.
2) along with fasting the day before it (Jumu’ah), this is permissible.
3) when it comes as the days of the middle of the month, the day of Arafah or ‘Aashooraa’, the six days of Shawwaal, or the first 9 days of thul-hijjah, then this is permissible, since he is not intending to fast because of the day being Saturday.
4) when it comes as a day that a person normally fasts, like the one who fasts every other day, this is permissible.
5) when a person intends to fast an optional fast because it is Saturday, and he singles it out, then this is the actual fasting on Saturday that is the focus of the prohibition.
May Allaah reward the shaykh and have mercy on him, for this is a good position as it allows for all the evidences to be acted upon in their right places in shaa’ Allaah.
And Allaah knows best.